Geodesic
On the rate of~approximation in the unit disc of~$H^1$-functions by logarithmic derivatives of~polynomials with zeros on the boundary
Izvestiya. Mathematics , Tome 84 (2020) no. 3, pp. 437-448

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We study uniform approximation in the open unit disc $D=\{z\colon |z|1\}$ by logarithmic derivatives of $C$-polynomials, that is, polynomials whose zeros lie on the unit circle $C=\{z\colon |z|\,{=}\,1\}$. We find bounds for the rate of approximation for functions in Hardy class $H^1(D)$ and certain subclasses. We prove bounds for the rate of uniform approximation (either in $D$ or its closure) by $h$-sums $\sum_k \lambda_k h(\lambda_k z)$ with parameters $\lambda_k\in C$.
Keywords: logarithmic derivative, simple partial fraction, uniform approximation, $h$-sum.
Mots-clés : $C$-polynomial 
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     author = {M. A. Komarov},
     title = {On the rate of~approximation in the unit disc of~$H^1$-functions by logarithmic derivatives of~polynomials with zeros on the boundary},
     journal = {Izvestiya. Mathematics },
     pages = {437--448},
     publisher = {mathdoc},
     volume = {84},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_3_a0/}
}
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M. A. Komarov. On the rate of~approximation in the unit disc of~$H^1$-functions by logarithmic derivatives of~polynomials with zeros on the boundary. Izvestiya. Mathematics , Tome 84 (2020) no. 3, pp. 437-448. http://geodesic.mathdoc.fr/item/IM2_2020_84_3_a0/